Ring arithmetic method, system, and apparatus

a ring arithmetic and operation technology, applied in the field of ring arithmetic operations, can solve the problems of increasing vulnerability, symmetric encryption is vulnerable, and many security challenges

Active Publication Date: 2003-03-06
NCIPHER LIMITED ACTING BY & THROUGH ITS WHOLLY OWNED SUBSIDIARY NCIPHER +1
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  • Summary
  • Abstract
  • Description
  • Claims
  • Application Information

AI Technical Summary

Problems solved by technology

Transmitting information over an open network--such as the Internet--involves many security challenges.
But symmetric encryption is vulnerable because communicants must share a private key.
But every session requires sharing of a new private key because key reuse would substantially increase vulnerability.
So in practice new sessions are established frequently, forcing heavy usage of asymmetric encryption.
Cryptanalyzing the encrypted message using

Method used

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  • Ring arithmetic method, system, and apparatus
  • Ring arithmetic method, system, and apparatus
  • Ring arithmetic method, system, and apparatus

Examples

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Embodiment Construction

[0137] A factor in slowing some public-private key cryptosystem processes is their requirement for modular exponentiation of large numbers. Even though this description most thoroughly focuses on encryption / decryption embodiments, many other embodiments are contemplated. Examples of other embodiments--readily apparent to typical practitioners of this technical area--include (1) tomography / transforming data, (2) decryption / encryption, (3) keyless encryption, (4) combination transforming / detransforming, (5) random number generation / monte carlo, (5) simulation of real-life scenarios, etc. Those applications typically require heavy exponentiation and for that and other reasons would be particularly well adapted to application of the present invention.

[0138] In an embodiment, shotgun multiplication is used to facilitate high security log-ins that use high-degree-sparse polynomials. One example is Purdy. See G. B. Purdy, "A high security log-in procedure", Communications of the ACM, 17 (1...

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Abstract

A data encryption method performed with ring arithmetic operations using a residue number multiplication process wherein a first conversion to a first basis is done using a mixed radix system and a second conversion to a second basis is done using a mixed radix system. In some embodiments, a modulus C is be chosen of the form 2w-L, wherein C is a w-bit number and L is a low Hamming weight odd integer less than 2(w-1)/2. And in some of those embodiments, the residue mod C is calculated via several steps. P is split into 2 w-bit words H1 and L1. S1 is calculated as equal to L1+(H12x1)+(H12x2)+ . . . +(H12xk)+H1. S1 is split into two w-bit words H2 and L2. S2 is computed as being equal to L2+(H22x1)+(H22x2)+ . . . +(H22xk)+H2. S3 is computed as being equal to S2+(2x1+ . . . +2xk+1). And the residue is determined by comparing S3 to 2w. If S3<2w, then the residue equals S2. If S3>2w, then the residue equals S3-2w.

Description

[0001] This application claims the benefit of the following U.S. Provisional Applications, all of which are hereby incorporated by reference, and the content of which are not necessarily identical to the content of this application:1 COMMONLY OWNED AND PREVIOUSLY FILED U.S. PROVISIONAL PATENT APPLICATIONS Atty. Dkt. # Ser. No. Title Filing Date 501143.000005 60 / 288,015 Method and Apparatus for Shotgun May 2, 2001 Multiplication and Exponentiation 501143.000010 60 / 300,957 Method and Residue Calculation Using Jun. 26, 2001 Casting Out 501143.000011 60 / 300,955 Add-Drop Layer 3 Ethernet Ring Switch Jun. 26, 2001 501431.000014 60 / 326,266 Application Specific Information Processing Oct. 1, 2001 System 501143.000015 60 / 326,252 Efficient Use of DRAM-Based Devices For Oct. 1, 2001 Small Discontiguous Memory Accesses 501143.000016 60 / 326,251 Exponentiation Engine Oct. 1, 2001 501143.000017 60 / 326,250 Method for Squaring Oct. 1, 2001[0002] The current application shares some specification and ...

Claims

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Application Information

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IPC IPC(8): G01N35/00G06FG06F7/72G06F12/00G06F13/00G06F13/16G06F13/28G06F15/16H04K1/00H04L9/28H04L12/28H04L12/56H04L29/06
CPCG01N2035/00247G01N2035/00574G06F7/72G06F7/723G06F7/727G06F7/728G06F13/1647G11C7/1066H04L47/125H04L63/0272H04L63/0428H04L63/166H04L9/302
Inventor BLAKLEY, GEORGE ROBERTDATTA, RAJATMITCHELL, OSCARSTEIN, KYLE
Owner NCIPHER LIMITED ACTING BY & THROUGH ITS WHOLLY OWNED SUBSIDIARY NCIPHER
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